if you create a new simple part that completely fills this space (plus more, some simple shape) - then use the Combine (subtract) function. This will let you cut the new part using the existing part. What you have left you simply use properties to see volume.
1) new sketch on bottom surface that is a rectangle slightly larger than your area in question as viewed from above
2) extrude up to surface (select the contour surface) (do not merge results)
3) insert -> feature -> combine -> subtract
4) Tools -> Mass Properties